خصوصیات عددی رفتار سازه از کلیسای پیلار در ساراگوسا (اسپانیا). قسمت 1: مدل های جهانی و محلی

The Basilica of Pilar, located in the city of Zaragoza, is one of the most famous Spanish temples. Several domes of this church contain frescoes painted by Francisco de Goya, which have suffered damages in the past decades due to various pathologies. The frescoes of the Regina Martirum dome are being restored at the present time. In this paper, we present a set of structural models of the entire temple and local models of the Regina Martirum dome by discussing and comparing the obtained results. The main objective of the research was to identify the current structural state of the church, its safety level and the relationship between the structural behaviour and the damages observed. The behaviour of the main material used in the construction, brick masonry, was simulated first with linear elastic isotropic models and later with several non-linear isotropic models including brittle behaviour in tension and plastic behaviour in compression. In addition, we consider the historical construction and the reinforcement works added to the structure in its history, with the purpose of testing the finite element models by reproducing the pathologies described from the beginning of the current Baroque construction.

The Basilica of Pilar is one of the most important worship places in Spain. The actual temple is a large complex brick masonry construction with rectangular plan of about 100 m long and 70 m wide. Their construction process was difficult and took long time [1]. In the current site, a small Visighotic chapel was first built more than a thousand years ago; then later on, it became a Romanesque church with cloister that suffered after the Gothic enlargement. Nevertheless, all the aforementioned constructions were small in size compared with the huge expansion taken place in XVII century when the Baroque church project was set up by the Spanish architect Ventura Rodriguez. In addition a reorientation to the main axis of the temple took place and part of the new construction was erected on terrain taken to the adjacent river. Fig. 1a presents a sketch describing the position of each building along the history and some plans; Fig. 2 shows several views of the actual Basilica.The temple is composed of three longitudinal naves (Fig. 1b). The central one contains the main dome of circular design and double shell, and two more domes of elliptical shape (Fig. 1d). The two lateral naves have eight more domes placed at a second level, the Regina Martirum dome belongs to this second level, located next to the central dome (Fig. 1c). Surrounding the principal naves there is a series of chapels and rooms with up to 11 additional domes at the third lower level. The domes at the third level are located between the 16 external buttresses and the four towers, of more than 90 m height, that mark the corners of the building and form the external perimeter. The central dome was erected by the middle of XIX century, and the first two towers of Pilar square façade were finalized at the end of the XIX century while the towers of Ebro river façade were erected in 1940.

The previous realization of a detailed geometrical model allowed us the generation of a complete FEM model with parametric meshing. • The study has permitted us to reproduce the historical pathologies of the basilica numerically, and to check out the efficiency of restoration works done in the past by the architect Teodoro Ríos between year 1927 and year 1940. • The use of linear models as a previous step to possible analyses considering more realistic non-linear models, allows us to comprehend the real structural behaviour, with less cost and complexity as compared to those of the non-linear cases. • Numerical models of the present state of the temple showed that the current structural situation of Regina Martirum dome is satisfactory and there is no risk of pathologies considering that the resistance to tension of the brick masonry is superior to 100 kPa. In the rest of the temple the structural situation is similar, except in the southern towers, where the existing compressive stresses due to its high elevation and the environment have deteriorated the brick masonry. They should be under observation to control their behaviour. • The obtained results are based on simplified material models with theoretical material parameter values obtained from the extensive existing bibliography. Because of the type of construction, its great dimensions, and the expanded temporary extension, it would be useful a future campaign of tests to determine accurately the mechanical properties of the masonry based on their deterioration degree and their spacing distribution, in order to determine the security level of the structure as well as assuring our assumptions. Also it was proposed that it is necessary to install some instruments to measure movements and fissure openings periodically, especially in the Regina Martirum dome. Furthermore, it would be advisable to install instruments, to determine the thermal loads and their variation. • With respect to numerical simulations in the future development, the following improvements are proposed: – Consideration of orthotropic behaviour of the masonry in the linear and non-linear models. – Use of a reduced rigidity matrix in the contour of the Regina Martirum dome base which replaces the displacements imposed in the non-linear analysis of the dome. – Application of a non-linear material model with distributed cracking in tension and plasticity to the complete model of the temple.